Calculation and control design of stability margins: a solution to singularly perturbed systems

Abstract

The theory of matrix perturbation is used to calculate the stability margins and design the feedback gain matrix which yields the specified stability margins for linear time-invariant multivariable systems. The calculation of stability margins is equivalent to the solution of a polynomial equation and the feedback gain design is equivalent to the problem of pole assignment. When these results are applied to singularly perturbed systems one will know why the stability of real dynamic systems can be analyzed from their mathematical models.<>